Mathematics, science and ontology

Synthese 88 (2):201 - 228 (1991)
  Copy   BIBTEX

Abstract

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section presents a way of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2009-01-28

Downloads
97 (#164,058)

6 months
4 (#319,344)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Ontological relativity and other essays.Willard Van Orman Quine (ed.) - 1969 - New York: Columbia University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Truth and other enigmas.Michael Dummett - 1978 - Cambridge: Harvard University Press.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.

View all 43 references / Add more references